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Mean field equilibria of dynamic auctions with learning

Mean field equilibria of dynamic auctions with learning Mean Field Equilibria of Dynamic Auctions with Learning KRISHNAMURTHY IYER and RAMESH JOHARI Stanford University and MUKUND SUNDARARAJAN Google Inc. We study learning in a dynamic setting where identical copies of a good are sold over time through a sequence of second price auctions. Each agent in the market has an unknown independent private valuation which determines the distribution of the reward she obtains from the good; for example, in sponsored search settings, advertisers may initially be unsure of the value of a click. Though the induced dynamic game is complex, we simplify analysis of the market using an approximation methodology known as mean eld equilibrium (MFE). The methodology assumes that agents optimize only with respect to long run average estimates of the distribution of other players ™ bids. We show a remarkable fact: in a mean eld equilibrium, the agent has an optimal strategy where she bids truthfully according to a conjoint valuation. The conjoint valuation is the sum of her current expected valuation, together with an overbid amount that is exactly the expected marginal bene t to one additional observation about her true private valuation. Under mild conditions on the model, we show that an MFE http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM SIGecom Exchanges Association for Computing Machinery

Mean field equilibria of dynamic auctions with learning

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2011 by ACM Inc.
ISSN
1551-9031
DOI
10.1145/2325702.2325705
Publisher site
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Abstract

Mean Field Equilibria of Dynamic Auctions with Learning KRISHNAMURTHY IYER and RAMESH JOHARI Stanford University and MUKUND SUNDARARAJAN Google Inc. We study learning in a dynamic setting where identical copies of a good are sold over time through a sequence of second price auctions. Each agent in the market has an unknown independent private valuation which determines the distribution of the reward she obtains from the good; for example, in sponsored search settings, advertisers may initially be unsure of the value of a click. Though the induced dynamic game is complex, we simplify analysis of the market using an approximation methodology known as mean eld equilibrium (MFE). The methodology assumes that agents optimize only with respect to long run average estimates of the distribution of other players ™ bids. We show a remarkable fact: in a mean eld equilibrium, the agent has an optimal strategy where she bids truthfully according to a conjoint valuation. The conjoint valuation is the sum of her current expected valuation, together with an overbid amount that is exactly the expected marginal bene t to one additional observation about her true private valuation. Under mild conditions on the model, we show that an MFE

Journal

ACM SIGecom ExchangesAssociation for Computing Machinery

Published: Dec 1, 2011

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